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Two-dimensional isometric tensor networks on an infinite strip
Abstract
The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an “orthogonality column” of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Finally, we introduce an infinite time-evolving block decimation algorithm (iTEBD2) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.
- Authors:
-
[1];
[2];
[3];
- Inst. of Physical and Chemical Research (RIKEN), Wako (Japan). Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS); Univ. of California, Berkeley, CA (United States)
- Univ. of California, Berkeley, CA (United States)
- Technische Univ., Munich (Germany)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)
- OSTI Identifier:
- 2234108
- Grant/Contract Number:
- AC02-05CH11231; SC0022716; BES-ERCAP0020043
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 107; Journal Issue: 24; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; quantum simulation; approximation methods for many-body systems; tensor network methods
Citation Formats
Wu, Yantao, Anand, Sajant, Lin, Sheng-Hsuan, Pollmann, Frank, and Zaletel, Michael P. Two-dimensional isometric tensor networks on an infinite strip. United States: N. p., 2023.
Web. doi:10.1103/physrevb.107.245118.
Wu, Yantao, Anand, Sajant, Lin, Sheng-Hsuan, Pollmann, Frank, & Zaletel, Michael P. Two-dimensional isometric tensor networks on an infinite strip. United States. https://doi.org/10.1103/physrevb.107.245118
Wu, Yantao, Anand, Sajant, Lin, Sheng-Hsuan, Pollmann, Frank, and Zaletel, Michael P. Fri .
"Two-dimensional isometric tensor networks on an infinite strip". United States. https://doi.org/10.1103/physrevb.107.245118.
@article{osti_2234108,
title = {Two-dimensional isometric tensor networks on an infinite strip},
author = {Wu, Yantao and Anand, Sajant and Lin, Sheng-Hsuan and Pollmann, Frank and Zaletel, Michael P.},
abstractNote = {The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an “orthogonality column” of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Finally, we introduce an infinite time-evolving block decimation algorithm (iTEBD2) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.},
doi = {10.1103/physrevb.107.245118},
journal = {Physical Review. B},
number = 24,
volume = 107,
place = {United States},
year = {Fri Jun 09 00:00:00 EDT 2023},
month = {Fri Jun 09 00:00:00 EDT 2023}
}
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